As far as I know, you don't need the water to finish the game but the higher level waters evaporate slower, cause less disease, and in general help the health of your plants. I found it helpful to have lvl 3 water.

As for the nets, I'm not skilled enough to catch the fast bugs with the lvl 2 net, I personally needed the full upgrade. But if you are quick and accurate, I think you could without.